Book IX in The Republic by Plato is mainly an argument to prove justice is better than injustice. Throughout the first part of Book IX, Socrates speaks about tyranny and the tyrannical man. Socrates proves that a tyrannical man (unjust man) leads the unhappiest of lives and therefore an aristocrat, being the just man, leads the happiest of lives. This is the first example that proves justice is better than injustice in Book IX. In the second part of Book IX, The Republic, Socrates provides a second argument for the conclusion that life is better as a just man than as an unjust man. Here, Socrates presents two new descriptions of a just and unjust man to replace the original images set forth in Book II. Socrates goes on to propose that every human lives with three animals inside him: a many headed beast, a lion, and a human being.
Each of these parts represents a different component of a man's soul. The human being represents reason and the ability to do so. The lion represents spirit and courage, and the many-headed beast represents uncontrollable desires. These three animals operate differently in the just man as opposed to the unjust man. For example, if a person behaves unjustly, these three animals are enemies to one another and do not function as a whole. This unjust man is "feeding" the beast and lion to make them stronger while he is starving the human being, thus making him weak. However, in the just man, all three parts operate as one and are friends with one another. In this scenario, the human being has the most power and treats the many-headed beast as a farm animal and takes care of it, preventing desires from taking over. The human being also takes the lion as an ally for protection. This example proves the just man happier than the unjust man.
Using this example, the unjust man is clearly worse off than the just man. By not controlling the many-headed beast, his desires have taken over.